Geometry · Trapezoid · Right triangle · Midpoints · Parallel lines
In a trapezoid \(ABCD\) with \(AB \parallel CD\), the two angles at the base \(AB\) add up to \(90^\circ\). Prove that the segment joining the midpoints of the two bases has length equal to half the difference of the bases.
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Serbian Municipal Competition 2001, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source